A multidimensional discontinuous Galerkin modeling framework for overland flow and channel routing

In this paper, we present the development and application of a new multidimensional, unstructured-mesh model for simulating coupled overland/open-channel flows in the kinematic wave approximation regime. The modeling approach makes use of discontinuous Galerkin (DG) finite element spatial discretizations of variable polynomial degree p, paired with explicit Runge-Kutta time steppers, and is supported by advancements made to an automatic mesh generation tool, Admesh +, that is used to construct constrained triangulations for channel routing. The developed modeling framework is applied to a set of four test cases, where numerical results are found to compare well with known analytic solutions, experimental data and results from another well-established (structured, finite difference) model within the area of application. The numerical results obtained demonstrate the accuracy and robustness of the developed modeling framework and highlight the potential benefits of using p (polynomial) refinement for hydrological simulations.